Which interval contains a local minimum for the grafted function? [-4, -2.5] [-2, -1] [1, 2] [2.5, 4]
1 answer:
Answer:
Last option [2.5, 4]
Step-by-step explanation:
The local minima of a function are the points where the slope of the curve is zero and the function reaches a minimum value.
If, on the contrary, the function reaches a maximum value, then that point is a local maximum.
Observe, for example, the point (3, -4). Note that a line tangent to that point would be horizontal, that is, of slope m = 0. This point is a minimum of the function, because there are no values x to the right x = 3 or to the left of x = 3 for which
Now we must search among the options that interval contains at this point.
The intervals [-4, -2.5] [-2, -1] do not contain any local minimum
The intervalor [1, 2] contains a local maximum.
The only interval that contains a local minimum is [2.5, 4], which contains the point (3, -4)
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Answer:
Step-by-step explanation:
We can do this a couple of ways. We can graph it -- see below. Or we can do the math.
Math
y = x^2 - 2x - 15
This trinomial factors into
y = (x - 5)(x + 3)
from which
x - 5= 0
x = 5
and
x + 3 = 0
x = - 3
The y intercept is the value obtained when all the xs on the right = 0
y = 0^2 - 2*0 - 15
y = - 15
<em>Answer</em>
- x intercepts: (-3,0),(5,0)
- y intercept: (0,-15)
The graph is below.
